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Consistent community detection in multi-layer networks with heterogeneous differential privacy

Yaoming Zhen, Shirong Xu, Junhui Wang

TL;DR

A personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable.

Abstract

As network data has become increasingly prevalent, a substantial amount of attention has been paid to the privacy issue in publishing network data. One of the critical challenges for data publishers is to preserve the topological structures of the original network while protecting sensitive information. In this paper, we propose a personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference. It can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable. Theoretically, we establish the consistency of community detection in the privatized multi-layer network and show that better privacy protection of edges can be obtained for a proportion of nodes while allowing other nodes to give up their privacy. Furthermore, the advantage of the proposed personalized edge-flipping mechanism is also supported by its numerical performance on various synthetic networks and a real-life multi-layer network.

Consistent community detection in multi-layer networks with heterogeneous differential privacy

TL;DR

A personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable.

Abstract

As network data has become increasingly prevalent, a substantial amount of attention has been paid to the privacy issue in publishing network data. One of the critical challenges for data publishers is to preserve the topological structures of the original network while protecting sensitive information. In this paper, we propose a personalized edge flipping mechanism that allows data publishers to protect edge information based on each node's privacy preference. It can achieve differential privacy while preserving the community structure under the multi-layer degree-corrected stochastic block model after appropriately debiasing, and thus consistent community detection in the privatized multi-layer networks is achievable. Theoretically, we establish the consistency of community detection in the privatized multi-layer network and show that better privacy protection of edges can be obtained for a proportion of nodes while allowing other nodes to give up their privacy. Furthermore, the advantage of the proposed personalized edge-flipping mechanism is also supported by its numerical performance on various synthetic networks and a real-life multi-layer network.
Paper Structure (13 sections, 6 theorems, 28 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 6 theorems, 28 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Background of Multi-layer Networks
  4. Differential Privacy
  5. Differential Privacy in Multilayer Networks
  6. Proposed Method
  7. Personalized Edge-flipping
  8. Decomposition after Debiasing
  9. Theory
  10. Numerical experiment
  11. Synthetic networks
  12. FriendFeed Multilayer Network
  13. Conclusions

Key Result

Lemma 1

The edge-flipping mechanism $\mathcal{M}_{\theta}$ satisfies $\epsilon$-edge local differential privacy when $\theta = \frac{e^{\epsilon}}{1+e^{\epsilon}}$.

Figures (5)

  • Figure 1: Averaged Hamming errors over 100 replications in Example 1.
  • Figure 2: Averaged Hamming errors over 100 replications in Example 2.
  • Figure 3: Averaged Hamming errors over 100 replications in Example 3.
  • Figure 4: The first 20 leading singular values of $\mathcal{M}_1(\bm{\mathcal{A}} \times_3 \bar{\bm{V}})$ in the FriendFeed multi-layer network.
  • Figure 5: The original 3-layer FriendFeed sub-network with 60 popular nodes (left), and a randomly selected flipped sub-network with $\beta = 10\%$ (right). Both panels consist of the following layer (blue), commenting layer (green), and liking layer (red).

Theorems & Definitions (11)

  • Definition 1: $\epsilon$-DP
  • Definition 2: $\epsilon$-LDP
  • Definition 3
  • Definition 4
  • Lemma 1
  • Definition 5
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Theorem 1
  • ...and 1 more